annual rent

[swapna]

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?

a.x>y
b.(xy/100)<x-y

ans b

can some one help?

[iamtensai]

This question took me a bit longer and I would have guessed on the exam. So i hope someone might have a faster solution.

here is my setup:
1997 rent : a
1998 rent : (1+x/100)a --> since 1998 rent is x percent more than 1997 rent
1999 rent : (1-y/100)(1+x/100)a --> since 1999 rent is y percent more than 1998 rent

the question is just asking us to compare "(1-y/100)(1+x/100)a" versus "a"

it simplifies to (1+x/100-y/100-xy/10000)a or (1+(x-y)/100-xy/10000)a

statement 1. x>y: insufficient. although we know that x-y>0, we don't know enough about the "xy/100" term.
statement 2. (xy/100)<x-y <=> (xy/10000)<(x-y)/100 <=> (x-y)/100-(xy/10000)>0, this address all our uncertainties and is sufficient.

[ajith]

Moved to DS forum

[eaakbari]

My method was the same as Iamtensai and yes I did cross 2. Do give alternate methods